Nicodemus spends about half of the book telling Mrs. Frisby his story, which is also the story of the other rats. When Nicodemus is the central narrator, it sounds like this:
"We lived near the market—my father, my mother, my nine sisters and brothers and I—underground in a big pipe that had once been part of a storm sewer, but wan no longer used." (14.25)
Having Nicodemus as a central narrator for the majority of the book is a cool feature mainly because his story is so engrossing. Animals, danger, drama, friendship? What's not to love? But it's also cool because, since it's told in flashback, we know that the rats make it out and are destined for awesomeness.
Nicodemus is a perfect central narrator because he knows which parts to highlight and which parts to skip over in order to explain it all to Mrs. Frisby in as clear and compelling a way as possible. But really, would you expect anything less from Nicodemus? We sure wouldn't.
The sections of the novel that aren't told in flashback are told in third person, limited omniscient. Take this as an example:
The room Mrs. Frisby entered was smaller than the library, but much more elegantly furnished […] But what attracted Mrs. Frisby's attention most was a box in one corner of the room. (11.18)
We don't know who the narrator is, but they seem to know a whole bunch about what the characters do, know, and think about, like here, when we can see "what attracted Mrs. Frisby." The fact that there are two different styles of narration going on in the story keeps the book moving along at a fast pace because if a reader ever gets bored reading about NIMH (as if!), Mrs. Frisby is sure to swoop back in and save the day in a chapter or so.